CONTINUUM FROM DISCONTINUUM

Discontinuing The Continuum, Replacing It By Quantum Entanglement Of Granular Substrate:

Is the universe granular? Discontinuous? Is spacetime somehow emergent? I do have an integrated solution to these quandaries, using basic mass-energy physics, and quantum entanglement. (The two master ideas I use here are mine alone, and if I am right, will change physics radically in the fullness of time.)

First let me point out that worrying about this is not just a pet lunacy of mine. Edward Witten is the only physicist to have got a top mathematics prize, and is viewed by many as the world’s top physicist (I have met with him). He gave a very interesting interview to Quanta Magazine: “A Physicist’s Physicist Ponders the Nature of Reality.

Edward Witten reflects on the meaning of dualities in physics and math, emergent space-time, and the pursuit of a complete description of nature.”

Witten: “I tend to assume that space-time and everything in it are in some sense emergent. By the way, you’ll certainly find that that’s what Wheeler expected in his essay [Information, Physics, Quantum, Wheeler’s 1989 essay propounding the idea that the physical universe arises from information, which he dubbed “it from bit.” He should have called it: “It from Qubit”. But the word “Qubit” didn’t exist yet; nor really the concept, as physicists had not realized yet the importance of entanglement and nonlocality in building the universe: they viewed them more as “spooky” oddities on the verge of self-contradiction. ..]

Edward Witten: As you’ll read, he [Wheeler] thought the continuum was wrong in both physics and math. He did not think one’s microscopic description of space-time should use a continuum of any kind — neither a continuum of space nor a continuum of time, nor even a continuum of real numbers. On the space and time, I’m sympathetic to that. On the real numbers, I’ve got to plead ignorance or agnosticism. It is something I wonder about, but I’ve tried to imagine what it could mean to not use the continuum of real numbers, and the one logician I tried discussing it with didn’t help me.”

***

Well, I spent much more time studying logic than Witten, a forlorn, despised and alienating task. (Yet, when one is driven by knowledge, nothing beats an Internet connected cave in the desert, far from the distracting trivialities!) Studying fundamental logic, an exercise mathematicians, let alone physicists, tend to detest, brought me enlightenment. mostly because it shows how relative it is, and how it can take thousands of years to make simple, obvious steps. How to solve this lack of logical imagination affecting the tremendous mathematician cum physicist Witten? Simple. From energy considerations, there is an event horizon to how large an expression can be written. Thus, in particular there is a limit to the size of a number. Basically, a number can’t be larger than the universe.

This also holds for the continuum: just as numbers can’t be arbitrarily large, neither can the digital expression of a given number be arbitrarily long. In other words, irrational numbers don’t exist (I will detail in the future what is wrong with the 24 century old proof, step by step).

As the world consists in sets of entangled quantum states (also known as “qubits”), the number of states can get much larger than the world of numbers. For example a set of 300 entangled up or down spins presents with 2^300 states (much larger than the number of atoms in the observable, 100 billion light years across universe). Such sets (“quantum simulators”) have been basically implemented in the lab.

Digital computers only work with finite expressions. Thus practical, effective logic uses already only finite mathematics, and finite logic. Thus there is no difficulty to use only finite mathematics. Physically, it presents the interest of removing many infinities (although not renormalization!)

Quantum entanglement creates a much richer spacetime than the granular subjacent space. Thus an apparently continuous spacetime is emergent from granular space. Let’s go back to the example above: 300 spins, in a small space, once quantum entangled, give a much richer spacetime quantum space of 2^300 states.

Consider again a set S of 300 particles (a practical case would be 300 atoms with spins up or down). If a set of “particles” are all entangled together I will call that a EQN (Entangled Quantum Network). Now consider an incoming wave W (typically a photonic or gravitational wave; but it could be a phonon, etc.). Classically, if the 300 particles were… classical, W has little probability to interact with S, because it has ONLY 300 “things”, 300 entities, to interact with. Quantum Mechanically, though, it has 2^300 “things”, all the states of the EQN, to interact with. Thus, a much higher probability of interacting. Certainly the wave W is more likely to interact wit2^300 entities than with 300, in the same space! (The classical computations can’t be made from scratch by me, or anybody else; but the classical computation, depending on “transparency” of a film of 300 particles would actually depend upon the Quantum computation nature makes discreetly, yet pervasely!

EQNs make (mathematically at least) an all pervasive “volume” occupying wave. I wrote “volume” with quote-unquote, because some smart asses, very long ago (nearly a century) pointed out that the Quantum Waves are in “PHASE” space, thus are NOT “real” waves. Whatever that means: Quantum volumes/spaces in which Quantum Waves compute can be very complicated, beyond electoral gerrymandering of congressional districts in the USA! In particular, they don’t have to be 3D “volumes”. That doesn’t make them less “real”. To allude to well-established mathematics: a segment is a one dimensional volume. A space filling curve is also a sort of volume, as is a fractal (and has a fractal dimension).

Now quantum entanglement has been demonstrated over thousands of kilometers, and mass (so to speak) quantum entanglement has been demonstrated over 500 nanometers (5,000 times the size of an atom). One has to understand that solids are held by quantum entanglement. So there is plenty enough entanglement to generate spaces of apparently continuous possibilities and even consciousness… from a fundamentally granular space.

Entanglement, or how to get continuum from discontinuum. (To sound like Wheeler.)

The preceding seems pretty obvious to me. Once those truths get around, everybody will say:’But of course, that’s so obvious! Didn’t Witten say that first?’

No, he didn’t.

You read it here first.

Granular space giving rise to practically continuous spacetime is an idea where deep philosophy proved vastly superior to the shortsightedness of vulgar mathematics.

28 Responses to “CONTINUUM FROM DISCONTINUUM”

Wow. Ever more creative. Could you specify how the states create the matter? Also looks like the states augment exponentially but then they are finite in number, still. Or is it just that there are much more?

OK, right, let me be more explicit. I will add the paragraph in the essays’ text.
Consider again a set S of 300 particles (a practical case would be 300 atoms with spins up or down). If a set of “particles” are all entangled together I will call that a EQN (Entangled Quantum Network). Now consider an incoming wave W (typically a photonic or gravitational wave; but it could be a phonon, etc.). Classically, if the 300 particles were… classical, W has little probability to interact with S, because it has ONLY 300 “things” to interact with. Quantum Mechanically, though, it has 2^300 “things”, the states of the EQN to interact with. A much higher probability.Certainly it’s more likely to interact wit2^300 than with 300, in the same space! (The classical computations can’t be made from scratch by me; but the classical computation, depending on “transparency” of a film of 300 particles would actually depend upon the Quantum computation nature makes!
Hoping that settles it.
For the continuum from discontinuum: actually the EQNs make (mathematically at least) an all pervasive “volume” occupying wave. I wrote “volume” because some smart asses, very long ago (nearly a century) pointed out that the Quantum Waves are in “PHASE” space. Whatever that means: Quantum volumes/spaces in which Quantum Waves compute can be very complicated, beyond electoral gerrymandering of congressional districts in the USA! In particular, they don’t have to be 3D “volumes”.

Yes. Please read my long answer to GMax. Actually I am going to graft part of it back into the essay, for greater thoroughness.
In a way of Quantum Physics is about how to get the continuum from the discontinuum, and back again. The last step being the coming into being, also known as “Singularization” (my semantics), or “localization” (my semantics), or “collapse of the wave packet” (traditional QM semantics, now controversial, because it exhibits the shortcoming of QM, as the “collapse” itself is NOT part of the QM theory: it’s needed, not described; I simply add 1) the requirement that collapse occurs at finite speed, 2) that causes an horizon threshold beyond which QM fails, causing DM and DE), or “decoherence” (recent euphemism central to Quantum computer engineering).

When you say that a number cannot be larger than the universe, do you meant that numbers cannot exceed the observable universe and therefore numbers cannot describe what may exist beyond the observable universe?
Or are you making a distinction between real numbers and irrational numbers for the purpose of distinguishing physics from mathematics? And if so, how does that help explain nature/reality?

Dear SDM: The essence of the argument is that a number which has more digits than there are states in the observable universe can’t be written down. And also that a number that can’t be written down does not exist. Now a mathematician could come and look at square root of two (the original irrational number). The Greeks wrote: (square root of 2) = a/b, where a and b are integers, and they found a contradiction. I will write the argument in more detail as an essay today (IF I find the time, not clear at all; then maybe tomorrow)
The argument is physico mathematics: the very notion of mathematics depends upon digits, and conventional logic which is also digital. Anyway, will try to detail…

I of course have assimilated much the same idea of a universe emergent from “the information field,” but always have in the back of my mind that we’re all just recapitulating Logos in a new form (“In the beginning was the Word, and the Word was God”), remaining true to our heritage of Western thought. This formulation puts all the cards in God’s hands, although the divinity leaves us “free will.”

This notion resembles *somewhat* the Eastern notion that Consciousness or godhead is the substrate of all, but is the “transmission mechanism” the same from God/Idea/Information to “Reality”? I don’t think so. The Eastern notion would seem to permit more engagement from our side, as observer effects wave collapse; that is, our Consciousness is entangled with godhead. (Some readings of the New Testament get us to much the same place.)

I never like the blahblah about “information” being fundamental. So no “information field” for me. In-formation, one could argue qubits have it. Yes they do. However, qubits are physical, “information”, as usually perceived, is not. The point, a point of mood, is subtle.
Nice you mention that, the “Logos”. The Quantum picture mangles the concept of Logos, generalizing it all over the place like sticky nonlocal elastic mud. Entangled Quantum Networks do NOT form a logos. They enable to singularize a logos somewhere.
In my vision of QM there is Dark matter, and Dark Energy. Is God Dark, or Energetic?
The “Eastern” notion of whatever is itself a form of “orientalism” (to steal Said, whom I don’t like very much). China is basically secular: none of the great mysticisms, not even Buddhism bit deep down there, except for Islam in Xinjiang and Lamaist hyper superstitious Buddhism in Tibet… both of which are not really China, and where few people live, and life is beautifully miserable.
I also need to do my traditional weekend baby apocalyptic run, that’s when I gather juice to confront the monsters out there, and deal with them as if they were cockroaches… (That’s why I will delay my demolition of square root of 2 proof, that being simply one of math’s most famous “proofs”…)
Cheers
Patrice

Isn’t the fact, that the Univers is governed according the law of mathematics an oddity, and not necessity of existence? How came these laws to existence? Maybe created by some kind of programmers? Maybe the programer made a mischief and enabled within the system under very certain conditions to come to existence life, consciousness, human intelligence all what we can observe on the earth? Maybe he is even watching his creation, that evolves independently from his original intention, to what his mischief will come too. Will it be destroyed by the humans? By wars using arms with global influence or by unrestrained population and economic growth, that will top over the cliff the system enabling uniquely on earth biological metabolism. Maybe the planetary systems life span is few billion years, but the human civilisation lifespan is not more than hundred years from the present? Then the programmer will say, puff, and have a great laugh.

Isn’t it annoying to think, that the whole human creation, including Bach, Mozart, Bethoven, but also Michalangelo, Picasso or Shakespeare, you name the rest is just a bug:-?.

And more, maybe the modernity with all the sciences, economic growth, technology, processes causing inbalancing to the global system, is just part of the joke of the programer, who was too bored by the ignorance of the humans, and decided to end the game ?
Am i too bleak?

To this i would reply, the ways of “God-programer” are incomprehensible. But again we are watching the existence from human perspective, even if systematically, with amazing instruments we developed. When religions like Judaism, Christianity, Islam were created, the only perspective humanity had was at human dimension of time and space. This is why earth was the center of everything and the world was created about 7000 years ago according to them. Galileo with his telescope started a proces that had changed all this. To believe in the bible as a book describing reality is denying the existence of telescope and the Large Hadron Collider, and other technological achievements the humanity created. There are religious Jews, Christians or Muslims who do just that. It is useless to try to speak to them. Those more sofisticated, creationists, thay still base their claims on human perception of time and space. Evolution is incomprehensible within human life and size span dimension.
Still, the science is limited to human comprehension, and within it there are too many opened issues, without which the chances that the humanity will exist beyond this century is rather unprobable. The global metabolic and environmental system is out of balance, and a big correction has to come. What shape this correction will take is a mystery. The humans have no tools to prevent it and also not to cope with it.

This question is just like the question who was first, chicken or the eggs. Mathematics is the only tool, that has the capacity to unveil to us the hidden reality of our existance. Take a program, consisting of binary codes, and it’s logical structure enabling to us to play a computer game. What is the reality in the game? The binary structure? The logical structure, that interconnects those binary codes in certain way and not other way? Or is it the game itself?

This analogy can be applied to the mathematics versus nature, while nature is the game, mathematics is the logical structure of its elements, meaning the numbers themselves and the capacity to add them to each other. All the rest comes out of it.
As to mathematics, two is more than one and one. It is also the meaning of + and =. When comprehending two, we comprehend all these elements. The + and = are as much elementary to mathematics as the 1.

Noone governs nobody. Not mathematics the nature and not vice versa. The nature just can’t be not logical not mathematical. Otherwise the chaos would take over the existence. Existence is order. Without order there wouldn’t be existence. Amazingly the Bible in it’s first sentence got it right. At beginning there was chaos, then by separation an order was created and the existence came to be. The order of nature is mathematical.

Interestingly an experiment somewhat reminiscent (but more complicated) of what I proposed back in September was “proposed” on ArchivX….

In SQPR, particles are pretty similar to what shows up on CERN screens: humps. Singularized humps of energy. Einstein says they stay lumpy, for ever and ever. I scoff, because, first of all, he literally didn’t know what he was talking about. (I propose to verify or dispel what he pontificated about!) QFT also pretty much posits the Einstein hypothesis. Let me scoff again (I took QFT classes in graduate school.) So where does the particle go? It disperses its energy field through the available (so-called “phase”) space at speed TAU (10^23 C, or so…) That’s why I proposed to conduct experiments. Nothing wrong with experiments. So-called “Higgs” theory for QFT, a detail relative to my own SQPR, is far from experimented-out: there may be several Higgs, etc.

Last comment: recently liberated from diurnal employment, I have been watching a lot of Dr Claude Swanson’s videos (books: Synchronized Universe, Life Force), who believes that the Russian theory of torsion fields accounts for most paranormal phenomena, quantum entanglement, etc., being the substrate beneath the quantum level permitting time reversal, non-locality, et al. Have you looked into this?

No. I don’t believe in “paranormal”. I also observed from close-by a would be star, professor Richard Muller, at UCB, who, jumped from one fashionable subject to the next, including so-called “psychophysics”. That was long ago. I objected to some of their alleged observed effects, explaining them with known physics, in particular optics. I was right, and nothing, indeed, came out of it…
Quantum Physics is plenty mysterious enough for my taste, and I have no doubt entanglement is involved in consciousness, and that we will create AC, Artificial Consciousness…

Liberated from “diurnal”? Now you only do nights??
BTW, “Torsion” has a strict mathematical meaning in differential geometry: one can have curvature without torsion, and reciprocally. Standard GR has zero torsion, it’s all about curvature.

You are too mainstream. There is ample evidence of psycho-kenesis by Jahn and Dunn and others, and of remote viewing by Puthoff and Targ. This is where the real action is, at the intersection of physics and philosophy. Look into torsion fields and see what you think (mainstream view via Wikipedia is “pseudoscience”.)

As I already said, Quantum Physics is way beyond anything imagined up to, say, 70 years ago. The NONLOCAL effects are many and can’t be disputed. But others can do like Benito Mussolini, and believe in all sorts of “rays”.
And as far as Puthoff and Targ, well, I was at Stanford U somewhat after they made fools of themselves with demonstrating Uri Geller “psychic” powers. They were at SRI (Stanford Research Institute), and those were not SRI days’ of glory…
Anyway, let me bask in the comfort of having being told I was “mainstream”. I was told all too many times by well-known mathematicians and philosophers that I was a monster, even abnormal by the most monstrous standards…

Being cheeky, yes, there might be 2^300 possible quantum states, and you can follow the proposition that they are superimposed (and nobody can prove you wrong because . . .) between your wave interacts with the system, does it not collapse to one state? While a spin might be up or down, your wave can only observe the discrete up or down but not both.

Incidentally big numbers have not scared off a lot of theorists. Thus you will see claims that enzymes evolved by chance. Now, suppose that is true, one of the first enzymes needed is one to break down failed and useless protein so that you can get more guesses. The probability of the more common enzyme to do that is 2 in 39^315, which is a somewhat bigger number. (Which is why I am convinced that hypothesis is wrong.)

Dear Ian: Thanks for the thoughtful feedback. The incoming wave W is itself in an UNCOLLAPSED STATE. It meets the uncollapsed wave of 2^300 states, call it S. W + S is itself a wave. Then it does its mysterious thing (I think it is a highly nonlinear mess, which thresholds of singularization if some curvature gets beyond a limit, a bit as if it were a black hole of sorts, but that’s irrelevant to the problem at hand). That mysterious thing leads to the quantum collapse of W + S on just one spin.
Very interesting what you say about enzymes. More water for my mill. Got to run, will get back to that latter

Fact is, the quantum wave, even if viewed only as a wave of knowledge, collapses. That’s weird. So was the wave not a wave of knowledge? Clearly nonlocal effects show that the fact ACTS AT A DISTANCE (this was shown explicitly by experiments of Zeillinger et al. in Austria; I think he got the Wolf Prize in physics for this and related work). What Einstein called “spooky interaction at a distance”. Einstein could view it as “incompleteness”, as he HOPED. However, we now know that there is no incompleteness in the sense that Quantum Mechanics overlooked a local hidden variable theory.
Countless Bell-Bohm EPR style experiments have demonstrated this conclusively. It turns out that NONLOCALITY is fundamental to biology, and, as all Quantum Computer engineers know, to the Quantum Computers (which are now real devices). OK, more later, I’am actually writing a full essay on it…

So let’s do some Einstein psychoanalysis here. Psychoanalysis is the number one weapon of philosophers.